In a recent work, we investigated the weak interaction of neutrinos in the homogeneous neutron-star (NS) matter within the framework of Korea-IBS-Daegu-SKKU (KIDS) density functional [1]}. The work focused on the effect of uncertainties and/or corrections of the nuclear matter equation of state (EoS), i.e., symmetry energy and nucleon effective mass, to the neutrino mean free path (NMFP) within the NS systematically. We found that the NMFP depends strongly on these uncertainties and/or corrections. Compared with the NS radius, the NMFP could be as short as about half of the NS radius, but also could be larger than the NS radius. Such wide range values of NMFP can lead to a different result in the cooling behavior of the NS. Overall, the work of Ref. [1]} demonstrated the importance of the accurate determination of nuclear matter EoS in the neutrino weak interaction at finite density and zero temperature. However, it is worth noting that in Ref. [1]}, the nucleons are treated as point particles, while, in fact, the nucleon has a structure such as the electromagnetic form factor in the transverse momentum and parton distribution functions in the longitudinal momentum. Such structure of the nucleon has been confirmed not only theoretically [4]}, but also experimentally [5]}, [6]}, [7]}, [8]}. Moreover, in the past, many studies have been done in investigating the neutral and charged current weak interaction of a neutrino with the matter by considering the electromagnetic form factor in the free space [9]}, [10]}, [11]}, [12]}, [13]}, [14]}. In the present work, we consider the structure of the nucleon–which is originally from non-perturbative quantum chromodynamic (QCD) aspect of hadron and particle physics in both free space and medium. It is well known that the electromagnetic form factors are expected to be modified in the medium [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}. Such medium effect can be non-negligible in the model [22]}, [23]}, providing another source of the corrections that can affect the NMFP.
